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Riesz's Rising Sun Lemma

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Riesz's sunrise lemma: Let be a continuous real-valued function on ℝ such that as and as . Let there exists with . Then is an open set, and if is a finite component of , then .

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The name of this lemma derives from the following: the sun is rising from the right in a mountainous region seen in a one-dimensional profile from the side. The elevation at is , and elements of are those values that remain in shadow at the instant the sun rises over the horizon as seen from .

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Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA

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